Quantitative constituent measurements in scattering media from statistical analysis of photon time-of-flight distributions

The long term goal of this project is to develop practical methods for quantitative measurements of constituents in scattering media. Pulsed femtosecond illumination and time-gated detection provide information about the photon pathlength. The photon time distribution is non-linearly dependent on three major parameters: the absorption cross-section, the scattering cross-section, and the phase function describing the degree of forward scattered light at each scattering event. To direct the construction of simplified instrumentation, we have investigated the use of analytic descriptors of the time distributions, such as derivatives and moments. Objective selection of the processing techniques were made using Stepwise Multi-Linear Regression to independently estimate the absorption and scattering coefficients. The method was tested with simulated time distributions. Results demonstrate that mean time of the trailing edge of the time profile can provide a quantitative estimation of the absorption coefficient when scattering is held constant. The second moment of the time profile provides the best estimator of the scattering coefficient with absorption held constant. When scattering and absorption vary simultaneously multiple parameters are required for quantitative estimates. The absorption coefficient estimates require the mean fall time, mean rise time, and the first moment of the distribution with variable scattering. The second moment, the mean rise time, the mean fall time, and the peak area provide the best estimates for the scattering coefficient with variable absorption. These results suggest that practical instrumentation may be developed which would allow for robust quantification in highly scattering media.